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Lagrangian Representation of the Family of Gordon–Schowalter Objective Derivatives at Simple Shear

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Moscow University Mechanics Bulletin Aims and scope

Abstract

The paper deals with the one-parameter family of Gordon–Schowalter objective derivatives including the Oldroyd, Cotter–Rivlin, and Jaumann derivatives. For a simple shear, movable bases are found in which the considered differential operators are reduced to the total time derivatives of the tensor components. For all derivatives of the family under consideration, except for Oldroyd and Cotter–Rivlin derivatives, the basis vectors lying in the shear plane rotate with a certain period changing their length and mutual orientation.

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Funding

The work is supported by the Russian Foundation for Basic Research (project no. 16-01-00669 A).

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Authors and Affiliations

  1. Chair of Theory of Elasticity, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

    E. D. Martynova

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  1. E. D. Martynova
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Correspondence to E. D. Martynova.

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Translated by E. Oborin

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Martynova, E.D. Lagrangian Representation of the Family of Gordon–Schowalter Objective Derivatives at Simple Shear. Moscow Univ. Mech. Bull. 75, 176–179 (2020). https://doi.org/10.3103/S0027133020060047

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  • DOI: https://doi.org/10.3103/S0027133020060047

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